A manufacture finds the total cost “C” for a product is expressed by C=3x2-8, and the total revenue “R” by R=3x-2, where x is the number of units sold. What is the breakeven point (where total cost=total revenue) to the nearest unit?
To find the breakeven point, we need to set the total cost (C) equal to the total revenue (R) and solve for x.
Given:
C = 3x^2 - 8
R = 3x - 2
Setting C equal to R:
3x^2 - 8 = 3x - 2
To solve this equation, we can rearrange it to form a quadratic equation:
3x^2 - 3x - 6 = 0
Now, we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 3, b = -3, and c = -6. Plugging in these values, we get:
x = (-(-3) ± √((-3)^2 - 4(3)(-6))) / (2(3))
x = (3 ± √(9 + 72)) / 6
x = (3 ± √81) / 6
x = (3 ± 9) / 6
This gives us two possible values for x:
x1 = (3 + 9) / 6 = 12 / 6 = 2
x2 = (3 - 9) / 6 = -6 / 6 = -1
Since we are looking for the number of units sold (which cannot be negative), the breakeven point is x = 2 units.